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«HIGHWAY INFRASTRUCTURE INTRODUCTION Highway infrastructure protection historically has been the primary consideration in determining TS&W limits as ...»

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States rate bridges, at their discretion, at either an inventory rating (55 percent of the yield stress) or operating rating (75 percent of the yield stress).5 Bridges are never intentionally loaded to yield stress in order to provide an adequate margin of safety. The design stress level for bridges is the same as the inventory rating, 55 percent of the yield stress. These two ratings are also used for posting bridges; either may be used under AASHTO guidelines, at the option of the State. A sign specifying weight limits is posted on bridges when it is determined that a vehicle above the specified weight would overstress the bridge. This weight could be that which stresses the bridge at either the 55 percent or 75 percent level of the yield stress.

AASHTO http://www2.epix.net/~lrfd/develop.html, February 19, 1998.


According to the AASHTO Manual for Maintenance Inspection of Highway Bridges (1983) an operating rating is defined as RF = 0.75-D/L(1+I) where RF= rating factor arrived at with the equation 0.55R= D + L (1 +

I) where R= the limiting stress (often the stress at which steel will undergo permanent deformation, or “yield”), D= stress due to dead load (the effect of gravity on bridge components), L= stress due to live load (vehicles on the bridge), I= an adjustment to the static effect of live loads to account for dynamic effects. An inventory bridge rating is arrived at by selecting the most highly stressed bridge component and inserting the rating factor (RF) into the Equation, RF= 0.55R- D/L(1 + I), as a multiplier on the live load of the rating truck.

VI-6 As States have the option to use either level for posting purposes, both ratings have been used in past studies to assess the bridge impacts for evaluating TS&W policy scenarios. Significant cost differences result from choice of rating. Use of the lower stress level (inventory rating) results in more bridges being identified as needing to be upgraded to accommodate increased weights or decreased lengths.6 Following the reviews of the TRB Special Reports 225 and 227 the FHWA determined that the stress level most representative of all State bridge posting practices was the inventory rating (55 percent of the yield stress) plus 25 percent, which gives a level of 68.8 percent of yield stress.

The FHWA used this 68.8 percent of yield to estimate the bridge cost impacts of LCVs. The resulting cost estimate reported by the FHWA in May 1991 was much closer to that based on the 75 percent rating, the TRB findings.


Bridge stresses caused by vehicles depend on both GVW and the distances between the axles that act as point loads. Trucks having equal weight but different wheelbases produce different bridge stresses. The shorter the wheelbase, the greater the stress. On a simple-span bridge, the length of a truck relative to the length of bridge span is also important. For relatively short spans (20 feet to 40 feet), all axles of a truck combination will not be on the bridge at the same time. The maximum bending moments determine stresses in the main load-carrying members of simple span bridges.

Figure VI-1 shows the maximum bending moments, by span lengths between 40 and 160 feet, for two trucks: a 50,000-pound single unit truck with a wheelbase of 19 feet, and an 80,000-pound combination with a wheelbase of 54 feet. For shorter bridges, the 50,000-pound single unit truck produces slightly higher stresses than the 80,000-pound combination; however, for longer bridges, the combination produces higher stresses.


The TS&W regulation to protect bridges generally takes the form of a bridge formula or table.

Federal bridge protection regulation, which became effective in 1975, uses a formula. Some States still use bridge tables, which were grandfathered by the 1975 Federal law. Other States use bridge tables for issuing overweight permits. The FBF is based on overstress criteria, the amount of bridge stress above the design stress to be allowed.

The TRB Special Reports 225, Truck Weight Limits: Issues and Options and 227, New Trucks for Greater Productivity and Less Road Wear: an Evaluation of the Turner Proposal estimated the bridge costs of the TS&W changes under study based on the operating rating of 75 percent of yield stress, whereas reviewers of those reports found much higher bridge costs resulting from the use of the inventory rating of 55 percent of yield stress.

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The level of risk to accept in determining acceptable loadings for a given bridge, or acceptable bridge design requirements for given loadings, is an element of TS&W regulation. A less conservative bridge formula, one that did not preserve the underlying FBF criteria, would reduce the margin of safety, thereby increasing somewhat the likelihood of bridge damage due to overstress. An overstress sufficient to damage a bridge would necessitate bridge repair and/or replacement sooner than anticipated.


Another factor to be considered is fatigue life, which is related to repetitive loadings. Each truck crossing produces one or more stress cycles in bridge components, which use up a portion of the components' fatigue lives. The magnitude of stress depends on vehicle weight and the size of the bridge component. The occurrence of a fatigue failure is signaled by cracks developing at points of high stress concentration.

Generally, only steel bridges are susceptible to fatigue, although some studies suggest that commonly used prestressed concrete spans, if overloaded, are similarly susceptible. The governing damage law for steel components has a third-power relationship between stress and damage, so that a doubling of stress causes an eight-fold increase in damage.7

Fisher, 1977.

VI-8 Bridge details that are particularly susceptible to fatigue include weld connections in tension zones, pin and hanger assemblies, and cover plates on the bottom flanges of steel beams.8 Many fatigue failures result from stresses induced indirectly by the distortion of the structure due to poor design details or unforeseen restraints. Most steel cracks reported to date probably fall into the category of distortion induced. Some of the worst detailing can be corrected by repair and retrofit.


In 1975 along with axle and maximum GVW limits for Interstate highways, Federal law adopted a bridge formula that restricts the maximum weight allowed on any group of consecutive axles based on the number of axles in the group and the distance from the first to the last axle. The AASHO proposed the formula concept in the 1940s. It was further developed and presented in a 1964 Report to Congress from the Secretary of Commerce.9 That Study recommended a table of maximum weights for axle groups to protect bridges (see Appendix A). The values in the table are

derived from the following formula, that is, FBF:

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Current Federal law specifies exceptions to the results given by the above formula: 68,000 pounds may be carried on two sets of tandem axles spaced at least 36 feet apart, and a single set of tandem axles spread no more than 8 feet is limited to 34,000 pounds.

The FBF is based on assumptions about the amount by which the design loading can be exceeded for different bridge designs. Specifically, this formula was designed to avoid overstressing HS-20 bridges by more than 5 percent and H-15 bridges by more than 30 percent.

The FHWA established a bridge stress level of not more than 5 percent over the design stress for HS-20 bridges to preserve the significantly large investment in these bridges by Federal, State, and local governments, and because these bridges carry high volumes of truck traffic.

AASHTO specifications give different allowable fatigue stresses for different categories of detail. These fatigue rules were initiated in the mid-1970s, therefore many older bridges were never checked during their original design for fatigue life. Further, the AASHTO fatigue rules apply to welded and bolted details with stresses induced directly by load passages (Moses, 1989).

Maximum Desirable Dimensions and Weights of Vehicles Operated on the Federal-Aid System, 1964 Study Report to Congress, U.S. Department of Commerce.

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The FBF reflects the fact that increasing the spacing between axles generally results in less concentrated loadings and lower stresses in bridge members. For example, the bridge formula would allow a 3-axle single-unit truck with a wheelbase of 20 feet to operate at 51,000 pounds. If the wheelbase of this truck is increased to 24 feet, the maximum weight allowed under FBF would increase to 54,000 pounds as shown in Table VI-2.

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20 51,000 55,500 60,500 24 54,000 58,000 63,000 28 57,000 60,500 65,500 32 60,000 63,500 68,000 36 66,000 70,500 40 68,500 73,000 As noted, there is a greater gain in allowable load by adding an axle than by increasing the distance between axles. For instance, at 30 feet a 3-axle vehicle is allowed a maximum GVW of 58,500 pounds and by adding 2 feet can gain only 1,500 pounds. If the same 3-axle vehicle at 30 feet adds an axle there is a gain of 3,500 pounds -- or 2,000 pounds more than by increasing distance by 2 feet. Increasing the number of axles in an axle group without increasing the overall length of the group has very little effect in reducing bridge stress. However, more axles do provide substantial benefits to pavements.


Actually, the FBF is not just one formula but a series of formulas with the appropriate one chosen by a parameter, N, the number of axles in the group in question. However, bridge stress is affected more by the total amount of load than by the number of axles. Thus the FBF is not effective in modeling the actual physical phenomenon, and it results in loads, especially for long combinations, that overstress bridges more than intended. More importantly, it encourages the addition of axles to obtain more payload even though one or both bridge stress criteria are exceeded. At other times, the equation restricts allowable loads for some short trucks below that Between the outside axles of any group of 2 or more axles.

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Since 1975, there have been a number of proposals to revise the FBF and reduce its shortcomings.

However, significant areas of concern have been identified with respect to the alternatives as well. Three alternative formulas proposed in recent years are discussed here: a TRB (a combination of the Texas Transportation Institute (TTI) and FBFs) alternative, an AASHTO alternative, and a Goshen alternative.


In 1990, the TRB recommended adoption of the formula developed by the TTI which would allow a 5 percent overstress for HS-20 bridges, in conjunction with existing Federal axle limits for vehicles with GVWs of 80,000 pounds or less.11 The TRB Report further recommended the FBF continue to be applied to vehicles weighing more than 80,000 pounds. The effect of this proposal would be an increase in maximum weights allowed for shorter vehicles, while the maximum weight limits for the longer wheelbase trucks would remain unchanged. It was asserted that the TTI formula was overly conservative at heavier weights.

The TTI formula is in the form of two equations for straight lines that meet at a wheelbase length of 56 feet.

For wheelbases less than 56 feet, it is:

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In 1993, AASHTO issued a report which recommended that its member committees (1) evaluate nationwide adoption of the TTI bridge formula as a replacement for FBF; (2) consider a limit on maximum extreme axle spacing of 73 feet in the short term; (3) retain existing single- and tandem-axle limits; (4) control tridem-axle weights -- and the special permitting of vehicles with GVWs more than 80,000 pounds -- using the original TTI bridge formula which protects both H-15 and HS-20 bridges, as opposed to the TTI formula mentioned above, which protects only HS-20 bridges. The recommendation was reviewed by the AASHTO Highway Subcommittees on Bridges and Structures and Highway Transport, accepted in resolution form, and approved by the Standing Committee on Highways. The AASHTO Board of Directors considered the recommendations at its 1996 Fall Meeting. The board expressed concern that the impact on pavements was not adequately addressed and remanded it for further consideration to the Subcommittees on Design and on Bridges and Structures.


In 1995 a research study by Ghosn and others for FHWA, proposed a new formula based on structural reliability theory as a replacement for the FBF.12 Structural reliability theory more explicitly accounts for the uncertainties associated with bridge design and load evaluation. The proposed formula, however, is considerably more permissive than the FBF when applied to long vehicles. It results in bridge stresses well above the criteria selected for this Study. Therefore, it was not considered.


Original research conducted for this Study suggests that a series of look-up tables may be developed based on the underlying the FBF stress criteria -- that is, a maximum overstress of 5 percent for HS-20 bridges, and 30 percent for H-15 bridges. These stresses were computed for both simple and continuous spans for the most critical span lengths for truck configurations.

The following discussion illustrates how this approach might be applied to three vehicles: (1) a tractor-semitrailer combination vehicle with a 3-axle tractor and 2-axle semitrailer, (2) a tractorsemitrailer combination vehicle with a 3-axle tractor and a semitrailer with a tridem-axle group, and (3) a RMD. The GVWs for each configuration with varying semitrailer lengths were calculated based on axle spacing.

Table VI-3 presents the weight values for the first vehicle combination under the FBF, TTI, and FBF stress criteria; and Figure VI-2 graphically displays maximum GVW from the Table, for semitrailers of varying lengths.

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